Problem Formulation & Method Solving in Artificial Intelligence (AI)

Problem Formulation in AI
Before an agent can start searching for solutions, it must formulate a goal and then use that goal to formulate a problem.

Problem Formulation & Method Solving in Artificial Intelligence (AI) organizes a number of steps to formulate a target/goals which require specific action to achieve the goal.

Hence, today, Problem Formulation & Method Solving in Artificial Intelligence is in use in various domains to formulate the goal on the basis of AI agents.

Hence, some methods used in Problem Formulation are :-

• Tree structure 

• Graphical model

• Implementation of graph

The Tree Structure

The Tree Structure

• Connected list, stack, and queue are 1-D data structures. 

• Hence, tree is a 2-D data structure. 

• Examples: 

– Family tree; 

– Tournament tree for a football game; 

– Organization tree of a company; and 

– Directory tree of a file management system. 

Useful terminologies  

• The nodes that have the same parent are known as Siblings.

• Path is a sequence of nodes(no. of nodes) connected by edges 

• Level of a node refers to the number of edges contained in the path hence from the root to this node 

• Height of the tree indicates maximum distance from the root to the terminal nodes

Terminologies in Tree Structure

Multi-way tree and binary tree 

• Multi-way tree or multi-branch tree 

– Hence, an internal node having more than 2 child nodes is known as a Multi-way tree or multi-branch tree.

– Hence, binary tree is useful both for information retrieval (binary search tree) and for pattern classification (e.g. decision tree). 

• Complete binary tree: 

– A binary tree is the one in which every node has 2 children. Hence, a binary tree is completely full, and nodes in the last level are as far left as possible.

Graphical Analysis

Graph structure 

• A graph is in use as 2-tuple where 𝑉 is a set of vertices or nodes; and 𝐸 is a set of edges, arcs, or connections. 

𝐺 = (𝑉, 𝐸)

where 𝑉 is a set of vertices or nodes; and 𝐸 is a set of edges, arcs, or connections.

• Hence, Tree is a special graph without cycles. 

– Hence, the path which the root forms is unique. 

Graph structure 

Adjacency-list representation

Graph Implementation 

• Adjacency-list representation: 

– N=|V|:number of nodes 

– Hence, we define N lists Adj[0], Adj[1], …, Adj[N-1] 

– Adj[i] is the list for the ith  node, which basically contains all nodes connected to this node by an edge. 

– That is, for any node j contained in Adj[i], (i,j) belongs to the set E of edges.

Adjacency-list representation: 

The above fig. explains the Adjacency-list representation.